where \(f\)  is induced by a Morse function on the circle \(\mathbb {T}\)  of reducible solutions on \(M_{\varphi }\) . We will show that for suitable choices of \(f,\delta \)  and \(\varepsilon \) , no irreducible solutions are introduced and one can achieve transversality in the sense of [1]}: the key issue here is to make sure that the perturbed Dirac operators at the reducible critical points has no kernel.
